A Motorcyclist Travels At A Speed Of 60km/h. How Long Will It Take To Cover A Distance Of 400m?
Introduction
In the realm of mathematics and physics, understanding the relationship between speed, distance, and time is crucial. This article delves into a practical problem involving a motorcyclist traveling at a constant speed. Our main objective is to determine the time it takes for the motorcyclist to cover a specific distance, given their speed. This problem is a classic example of applying basic kinematic principles, which are fundamental in understanding motion. We will explore the concepts of speed, distance, and time, and how they interrelate to solve this problem. This problem not only reinforces mathematical skills but also provides a real-world application of these concepts, making learning more engaging and relevant.
Problem Statement
The core of our discussion lies in the following scenario: a motorcyclist is traveling at a speed of 60 kilometers per hour (km/h). The question we aim to answer is: how much time will it take for this motorcyclist to cover a distance of 400 meters? This problem requires us to apply our understanding of the relationship between speed, distance, and time. The challenge lies in the fact that the speed is given in kilometers per hour, while the distance is in meters. To accurately solve the problem, we need to ensure that all units are consistent. This often involves converting kilometers per hour to meters per second, which is a crucial step in solving many physics and mathematics problems related to motion. The careful conversion of units ensures that our calculations are accurate and the final answer is meaningful.
Breaking Down the Problem
To tackle this problem effectively, we need to break it down into smaller, more manageable steps. Firstly, we identify the given information: the speed of the motorcyclist (60 km/h) and the distance to be covered (400 meters). The unknown variable we need to find is the time taken. The key to solving this problem lies in the formula that relates speed, distance, and time: speed = distance / time. However, before we can apply this formula, we need to address the issue of inconsistent units. The speed is given in km/h, while the distance is in meters. To maintain consistency, we need to convert the speed from km/h to meters per second (m/s). This conversion involves multiplying the speed in km/h by a conversion factor. Once we have the speed in m/s and the distance in meters, we can rearrange the formula to solve for time: time = distance / speed. This step-by-step approach allows us to systematically solve the problem and arrive at the correct answer.
Unit Conversion: Kilometers per Hour to Meters per Second
In this section, we will focus on the crucial step of converting the speed from kilometers per hour (km/h) to meters per second (m/s). This conversion is essential because the distance is given in meters, and to accurately calculate the time, we need both speed and distance to be in compatible units. The conversion factor between km/h and m/s is derived from the fact that 1 kilometer is equal to 1000 meters, and 1 hour is equal to 3600 seconds. Therefore, to convert km/h to m/s, we multiply the speed in km/h by 1000/3600, which simplifies to 5/18. This conversion factor is a fundamental tool in physics and is frequently used in problems involving motion. Applying this conversion factor correctly is critical for obtaining the correct solution. Understanding the basis of this conversion not only helps in solving this particular problem but also enhances the understanding of unit conversions in general, which is a valuable skill in various scientific and engineering fields.
Step-by-Step Conversion
Let's delve into the step-by-step process of converting 60 km/h to m/s. First, we start with the given speed: 60 km/h. To convert this to m/s, we multiply by the conversion factor 5/18. This can be written as: 60 km/h * (5/18). Performing this calculation, we get: (60 * 5) / 18 = 300 / 18. Simplifying this fraction, we find that 300 / 18 equals approximately 16.67 m/s. Therefore, 60 km/h is equivalent to 16.67 m/s. This conversion is a critical step in our problem-solving process, as it ensures that the units of speed and distance are consistent, allowing us to accurately calculate the time. Understanding this conversion process is not just about arriving at the correct numerical answer; it's about grasping the underlying principles of unit conversion, which is a fundamental skill in physics and engineering. The ability to confidently convert between different units is essential for solving a wide range of problems and for interpreting scientific data.
Calculating the Time
With the speed now converted to meters per second (m/s), we can proceed to calculate the time it will take for the motorcyclist to cover the distance of 400 meters. As established earlier, the formula that relates speed, distance, and time is: speed = distance / time. To find the time, we need to rearrange this formula to solve for time: time = distance / speed. We now have the distance (400 meters) and the speed (16.67 m/s, as calculated in the previous section). Plugging these values into the formula, we get: time = 400 meters / 16.67 m/s. This calculation will give us the time in seconds, which is the unit of time consistent with our units of distance and speed. The ability to rearrange formulas and substitute values is a core skill in mathematics and physics, and this step demonstrates the practical application of this skill in solving a real-world problem.
Applying the Formula
Now, let's apply the formula time = distance / speed with the values we have. The distance is 400 meters, and the speed is 16.67 m/s. Substituting these values into the formula, we get: time = 400 / 16.67. Performing this division, we find that the time is approximately 24 seconds. This result tells us that it will take the motorcyclist approximately 24 seconds to cover the distance of 400 meters while traveling at a speed of 60 km/h (or 16.67 m/s). This calculation provides a concrete answer to our initial question and highlights the practical application of the concepts of speed, distance, and time. The ability to accurately calculate time given speed and distance is not only useful in academic contexts but also has real-world applications in fields such as transportation, logistics, and sports, where understanding the dynamics of motion is essential.
Conclusion
In conclusion, we have successfully calculated the time it takes for a motorcyclist traveling at 60 km/h to cover a distance of 400 meters. By carefully converting the speed from kilometers per hour to meters per second and applying the formula time = distance / speed, we determined that the motorcyclist will take approximately 24 seconds to cover the specified distance. This problem underscores the importance of unit consistency in calculations and demonstrates the practical application of fundamental physics concepts. Understanding the relationship between speed, distance, and time is crucial in various real-world scenarios, from planning travel routes to understanding the dynamics of moving objects. This exercise not only reinforces mathematical and physics skills but also highlights the relevance of these concepts in everyday life. The ability to solve problems like this is a testament to the power of mathematical reasoning and its ability to provide insights into the world around us.
Key Takeaways
The key takeaways from this problem-solving exercise are multifaceted. Firstly, we've reinforced the understanding of the fundamental relationship between speed, distance, and time, as expressed by the formula speed = distance / time. Secondly, we've highlighted the critical importance of unit consistency in calculations. The conversion from kilometers per hour to meters per second was a pivotal step in solving the problem accurately. Thirdly, we've demonstrated the practical application of mathematical and physics concepts in a real-world scenario. This problem illustrates how abstract concepts can be used to solve tangible problems. Furthermore, we've emphasized the importance of breaking down complex problems into smaller, more manageable steps. By systematically addressing each step, from unit conversion to formula application, we were able to arrive at the correct solution. Ultimately, this exercise underscores the value of problem-solving skills and the ability to apply mathematical and scientific principles to understand and analyze the world around us.